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12.3. Practice Sets: Transmitting rotational motion through gears

Chapter Equations

[latex]\small N \times T = n \times t[/latex] (1)

[latex]\small N \times T_1 \times T_2 \times T_3 \times \cdots = n \times t_1 \times t_2 \times t_3 \times \cdots[/latex] (2)

Try it!

  1. A driven gear has triple the number of teeth as the driver gear. What is the ration between the rotational speeds of the driven and driven gears?
  2. A gear cannot be a driver and a driven at the same time. True or false?
  3. Two gears that are positioned on the same shaft (do not mesh with each other) do not have a driver/driven relationship. (True or false?)

Practice

  1. Gear A has [latex]35 \text{ teeth}[/latex] and rotates at [latex]35 \text{rpm}[/latex]; gear B has [latex]23 \text{ teeth}[/latex], and gear C has [latex]11 \text{ teeth}[/latex]. Given the gear train below, find:
    The largest orange gear (A) rotates counterclockwise, as indicated by an arrow. A medium-sized red gear (B), meshed with the orange one, rotates clockwise. A smaller yellow gear (C), meshed with the red gear, rotates counterclockwise
    1. The rotational speed of gear C in [rpm]
      Answer:

      [latex]111.4 \text{ rpm}[/latex]
    2. The angular velocity of gear A in [rad/s]
      Answer:

      [latex]3.7 \text{ rad/s}[/latex]
  2. Given the train gear below, find the rotational speed of gear A. The last driven wheel (gear C) rotates at [latex]120 \text{ rpm}[/latex] and has [latex]37 \text{ teeth}[/latex]. Gear A has [latex]73 \text{ teeth}[/latex] and gear B has [latex]39 \text{ teeth}[/latex].

    Answer:

    [latex]113.8 \text{ rpm}[/latex]
  3. Gear A has [latex]34 \text{ teeth}[/latex] and rotates at [latex]340 \text{ rpm}[/latex]; gear B has [latex]24 \text { teeth}[/latex]; gear C has [latex]47 \text{ teeth}[/latex]; gear D has [latex]19 \text{ teeth}[/latex]. Given the gear train below find:

    1. The rotational speed of bear D in [rad/s]
      Answer:

      [latex]124.8 \text{ rad/s}[/latex]
    2. The rotational speed of gear B in [rpm]
      Answer:

      [latex]481.7 \text{ rpm}[/latex]

Challenge Questions

Gear A meshes with gear B as shown in the figure below. If A starts from rest and has a constant angular acceleration of [latex]\alpha_A = 1.5 \, \text{rad/s}^2[/latex], determine the time needed for B to reach an angular velocity of [latex]\omega_B = 45 \, \text{rad/s}[/latex].

Answer:

[latex]75 \, \text{s}[/latex]
Text Version of the Challenge Question(s)
  • Gear A meshes with gear B as shown in the figure below. If A starts from rest and has a constant angular acceleration of [latex]\alpha_A = 1.5 \, \text{rad/s}^2[/latex], determine the time needed for B to reach an angular velocity of [latex]\omega_B = 45 \, \text{rad/s}[/latex].
    Answer: [latex]75 \, \text{s}[/latex]

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College Physics – Fundamentals and Applications Copyright © by Daniela Stanescu, Centennial College is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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